Content Area: Math

 

Index: 4.3A Grade 12 CPI 4

 

Standard: 4.3 - Patterns and Algebra

 

Strand: A - Patterns

 

Cumulative Progress Indicator: 4 - The student will understand and compare the properties of classes of functions, including exponential, polynomial, rational, and trigonometric functions

·        Linear vs. non-linear

·        Symmetry

·        Increasing/decreasing on an interval

 

Grade: 12

 

Sample Activities:

 

·        On a test, students are asked to determine the truth value of the statement "log x > 0 for all positive real numbers x." One student remembers that log x is the exponent to which 10 must be raised to get x, and to get a number less than 1 would require a negative exponent. Another student picks some trial points, develops a chart of the points and their logarithms and discovers that when x < 1, log x < 0. A third student graphs the function on his graphing calculator and sees that when x < 1, the graph of log x is below the x axis.

 

Sample Assessment Questions:

 

·        Marie has been driving at a constant speed along the New Jersey Turnpike. The distance she travels depends on how long she has been driving. If you were to attempt to graph the distance Marie has driven as a function of time, what type of function would it be? 

o       a. Exponential

o       b. Linear 

o       c. Periodic 

o       d. Quadratic 

 

The correct answer is B.